Answer:
The equation of the parabola is y=(1/8)x^2
[tex]y=\dfrac{1}{8}x^2[/tex]
Step-by-step explanation:
We know the vertex (0,0) and the focus (0,2) of the parabola.
The equation in vertex form is written as:
[tex]y=a(x-h)^2+k\\\\\text{vertex}=(h,k)[/tex]
Then, in this case, we have the equation:
[tex]y=a(x-0)^2+0=ax^2[/tex]
As the focus is (0,2), it is at a distance of 2 units from the vertex (0,0).
For the focus, we have the following equation:
[tex]4p(y-k)=(x-h)^2[/tex]
where p is the distance from the focus to the vertex (in this case, p=2).
h and k are the vertex coordinates, both 0.
So we have:
[tex]4p(y-k)=(x-h)^2\\\\4(2)(y-0)=(x-0)^2\\\\8y=x^2\\\\y=\dfrac{1}{8}x^2[/tex]
